Bayesian regression on non-parametric mixed-effect models with shape-restricted Bernstein polynomials

Jianhua Ding and Zhongzhan Zhang

Journal of Applied Statistics, 2016, vol. 43, issue 14, 2524-2537

Abstract: We develop a Bayesian estimation method to non-parametric mixed-effect models under shape-constrains. The approach uses a hierarchical Bayesian framework and characterizations of shape-constrained Bernstein polynomials (BPs). We employ Markov chain Monte Carlo methods for model fitting, using a truncated normal distribution as the prior for the coefficients of BPs to ensure the desired shape constraints. The small sample properties of the Bayesian shape-constrained estimators across a range of functions are provided via simulation studies. Two real data analysis are given to illustrate the application of the proposed method.

Date: 2016
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DOI: 10.1080/02664763.2016.1142940

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